Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#11929434 | C2 | semidirect |
| 3. #23757241 | C2 | direct (N × H) |
| 4. C2×#19097683 | C2 | semidirect |
| 5. C22×M16×C157 | C2 | semidirect |
| 16. C22×#11929434 | C22 | semidirect |
| 17. #19097683 | C22 | semidirect |
| 20. C2×M16×C157 | C22 | semidirect |
| 91. C2×C157 | #408 | semidirect |
| 95. C157 | C2×#408 | semidirect |
| 98. C22×M16 | D157 | semidirect |
| 112. C2×M16 | C2×D157 | semidirect |
| 188. C2 | #23757241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578954 | 2 |
| C23×#11929434 | 2 |
| #23757241 | 2 |
| C2×#19097683 | 2 |
| C22×M16×C157 | 2 |
| C2×#408 | 157 |